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100 points for $49 worth of Veritas practice GMATs FREE VERITAS PRACTICE GMAT EXAMS Earn 10 Points Per Post Earn 10 Points Per Thanks Earn 10 Points Per Upvote ## A book has 1000 pages numbered 1, 2, 3, â€¦, and so on. How tagged by: Max@Math Revolution ##### This topic has 2 expert replies and 0 member replies ### GMAT/MBA Expert ## A book has 1000 pages numbered 1, 2, 3, â€¦, and so on. How ## Timer 00:00 ## Your Answer A B C D E ## Global Stats Difficult [GMAT math practice question] A book has 1000 pages numbered 1, 2, 3, â€¦, and so on. How many times does the digit 2 appear on the page numbers? A. 200 B. 250 C. 300 D. 400 E. 500 _________________ Math Revolution Finish GMAT Quant Section with 10 minutes to spare. The one-and-only Worldâ€™s First Variable Approach for DS and IVY Approach for PS with ease, speed and accuracy. Only$149 for 3 month Online Course
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Max@Math Revolution wrote:
[GMAT math practice question]

A book has 1000 pages numbered 1, 2, 3, â€¦, and so on. How many times does the digit 2 appear on the page numbers?

A. 200
B. 250
C. 300
D. 400
E. 500
Ignore page 1000, since it does not include the digit 2.
To make the calculation easier, consider the remaining pages numbered as 3-digit integers, beginning with 000 and ending with 999:
000, 001, 002...997, 998, 999

There are 1000 options between 000 to 999, inclusive.
Since each option is composed of 3 digits, the total number of digits = 3*1000 = 3000.
The probability that 2 will appear in any given position is the same as the probability that 3 will appear in any given position.
Implication:
Each of the 10 digits 0 through 9 will appear the SAME NUMBER OF TIMES.
Thus, the number of times that 2 will appear = 3000/10 = 300.

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The page numbers 2, 12, 20, 21, 22, â€¦ , 29, 32, 42, â€¦ , 92 contain 19+1 = 20 copies of the digit, 2.
The page numbers 102, 112, 120, 121, â€¦ , 129, 132, 142, â€¦ , 192 similarly contain 20 copies of the digit 2.
The page numbers 200, 201, â€¦ , 299 contain 120 copies of the digit, 2.
Page numbers 302, 312, 320, 321, â€¦ , 329, 332, 342, â€¦ , 392 contain 20 copies of the digit, 2.
â€¦
Page numbers 902, 912, 920, 921, 922, â€¦ , 929, 932, 942, â€¦ , 992 contain 20 copies of the digit, 2.

The total number of copies of the digit, 2 printed on the pages is
9*20 + 120 = 300.

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